Apparatus for ultrasound flow vector imaging and methods thereof

ABSTRACT

Apparatus and methods of use are provided for complex flow imaging and analysis that is non-invasive, accurate, and time-resolved. It is particularly useful in imaging of vascular flow with spatiotemporal fluctuations. This apparatus is an ultrasound-based framework called vector projectile imaging (VPI) that can dynamically render complex flow patterns over an imaging view at millisecond time resolution. The VPI apparatus and methods comprise: (i) high-frame-rate broad-view data acquisition (based on steered plane wave firings); (ii) flow vector estimation derived from multi-angle Doppler analysis (coupled with data regularization and least-squares fitting); and (iii) dynamic visualization of color-encoded vector projectiles (with flow speckles displayed as adjunct).

The present application claims priority to U.S. Provisional ApplicationNo. 61/905,974 filed on Nov. 19, 2013, which is incorporated herein inits entirety.

TECHNICAL FIELD

The present invention is generally directed to an ultrasonic imagingsystem, and more particularly to an ultrasonic system for imagingvascular flow. This imaging system can be used for non-invasivelyvisualizing the flow of blood in a human blood vessel.

BACKGROUND OF THE INVENTION

Non-invasive visualization of flow dynamics in human arteries is widelyconsidered to be of high diagnostic importance as it may foster clinicaldetection of abnormal vascular conditions (Steinman D A, Taylor Calif.Flow imaging and computing: large artery hemodynamics. Ann. Biomed.Eng., 2005; 33: 1704-1709). For instance, monitoring flow patterns inthe carotid arteries has long been implicated in useful in strokeprognosis (Donnan G A, Fisher M, Macleod M, Davis S M. Stroke. Lancet,2008; 371: 1612-1623; Shields R C. Medical management of carotidstenosis. Perspect. Vasc. Surg. Endovasc. Ther., 2010; 22: 18-27). Overthe years, a few non-invasive flow imaging modalities have beendeveloped (Owen A R, Roditi G H. Peripheral arterial disease: theevolving role of non-invasive imaging. Postgrad. Med. J., 2011; 87:189-198; Wolbarst A B, Hendee W R. Evolving and experimentaltechnologies in medical imaging. Radiology, 2006; 238: 16-39), and amongthem, ultrasound has perhaps established itself as a unique bedsidemodality that can be readily applied to point-of-care diagnoses (BierigS M, Jones A. Accuracy and cost comparison of ultrasound versusalternative imaging modalities, including CT, MR, PET, and angiography.J. Diagnost. Med. Sonography, 2009; 25: 138-144; Moore C L, Copel J A.Point-of-care ultrasonography. New Eng. J. Med., 2011; 364: 749-757). Inmost existing ultrasound scanners, flow information can be rendered inreal-time in the form of color flow images, which provide 2-D maps ofaxial flow velocity (or flow power) over an imaging view (Evans D H.Color flow and motion imaging. Proc. Inst. Mech. Eng. H, 2010; 224:241-253; Hoskins P R, McDicken W N. Colour ultrasound imaging of bloodflow and tissue motion. Br. J. Radiol., 1997; 70: 878-890). This flowimaging mode, when used together with the Doppler spectrogram mode thatplots the temporal flow profile at a single range gate, can offer vastinformation about flow behavior in both spatial and temporal dimensions(Gaitini D, Soudack M. Diagnosing carotid stenosis by Dopplersonography: state of the art. J. Ultrasound Med., 2005; 24: 1127-1136;Hoskins P R. Haemodynamics and blood flow measured using ultrasoundimaging. Proc. Inst. Mech. Eng. H, 2010; 224: 255-271).

Despite its popular role in clinical screening, ultrasound color flowimaging is known to possess method flaws (Evans 2010). In particular, asits operating principle is typically based on axial Doppler estimation,it is prone to error if the beam-flow angle (i.e. angle between theultrasound propagation axis and the flow trajectory) varies over thevasculature (Evans D H, Jensen J A, Nielsen M B. Ultrasound colorDoppler imaging. Interface Focus, 2011; 1: 490-502). This issuerepresents a significant pitfall in diagnostic scenarios where thevasculature is not in straight-tube form, such as the bifurcationgeometry found in the carotid arteries (Ku D N. Blood flow in arteries.Annu. Rev. Fluid Mech., 1997; 29: 399-434). In these cases, it can bechallenging for sonographers to properly interpret color flow images(Arning C, Eckert B. The diagnostic relevance of colour Dopplerartefacts in carotid artery examinations. Eur. J. Radiol., 2004; 51:246-251; Rubens D J, Bhatt S, Nedelka S, Cullinan J. Doppler artifactsand pitfalls. Radiol. Clin. N. Am., 2006; 44: 805-835), especially whenexacerbated by pulsatile flow conditions with considerable temporalvariations in flow velocities.

For ultrasound to succeed in providing unambiguous mapping of flowdynamics in tortuous vasculature, it is imperative to resolve thebeam-flow angle dependence problem and in turn derive velocity estimatesthat reflect the actual flow characteristics (Dunmire B, Beach K W, LabsK H, Plett M, Strandness Jr D E. Cross-beam vector Doppler ultrasoundfor angle-independent velocity measurements, Ultrasound Med. Biol.,2000, 26: 1213-1235; Tortoli P, Bambi G, Ricci S. Accurate Doppler angleestimation for vector flow measurements. IEEE Trans. Ultrason.Ferroelec. Freq. Contr., 2006; 53: 1425-1431; Tortoli P, Dallai A, BoniE, Francalanci L, Ricci S., “An automatic angle tracking procedure forfeasible vector Doppler blood velocity measurements,” Ultrasound Med.Biol. (2010), 36: 488-496). To fulfill this task, flow estimation needsto be performed not only along the axial direction (as is the case incolor flow imaging) but also the lateral direction of the imaging view,so that both the flow angle and the velocity magnitude can be determinedwithout uncertainty (Evans et al. 2011). Motivated by such rationale,new imaging paradigms for flow vector estimation have been proposed.Often categorized as vector flow imaging methods, these paradigms aregenerally based on four types of estimation principles: (i) multi-angleDoppler analysis (Capineri L, Scabia M, Masotti L. A Doppler system fordynamic vector velocity maps. Ultrasound Med. Biol., 2002; 28: 237-248;Kripfgans O D, Rubin J M, Hall A L, Fowlkes J B. Vector Doppler imagingof a spinning disc ultrasound Doppler phantom. Ultrasound Med. Biol.,2006; 32: 1037-1046; Pastorelli A, Torricelli G, Scabia M, Biagi E,Masotti L. A real-time 2-D vector Doppler system for clinicalexperimentation. IEEE Trans. Med. Imag., 2008; 27: 1515-1524; (ii)biaxial phase shift estimation from acoustic fields with transverseoscillations (Pedersen M M, Pihl M J, Haugaard P, Hansen J M, Hansen KL, Nielsen M B, Jensen J A. Comparison of real-time in vivo spectral andvector velocity estimation. Ultrasound Med. Biol., 2012; 39: 145-151;Udesen J, Jensen J A. Investigation of transverse oscillation method.IEEE Trans. Ultrason. Ferroelec. Freq. Contr., 2006; 53: 959-971; UdesenJ, Nielsen M B, Nielsen K R, Jensen J A. Examples of in vivo bloodvector velocity estimation. Ultrasound Med. Biol., 2007; 33: 541-548);(iii) inter-frame blood speckle tracking (Bohs L N, Geiman B J, AndersonM E, Gebhart S C, Trahey G E. Speckle tracking for multi-dimensionalflow estimation. Ultrasonics, 2000; 38: 369-375; Ebbini E S.Phase-coupled two-dimensional speckle tracking algorithm. IEEE Trans.Ultrason. Ferroelec. Freq. Contr., 2006; 53: 972-990; Xu T, Bashford GR. Two-dimensional blood flow velocity estimation using ultrasoundspeckle pattern dependence on scan direction and A-line acquisitionvelocity. IEEE Trans. Ultrason. Ferroelec. Freq. Contr., 2013; 60:898-908); and (iv) directional cross-correlation analysis (Jensen J A.Directional velocity estimation using focusing along the flow directionI: theory and simulation. IEEE Trans. Ultrason. Ferroelec. Freq. Contr.,2003; 50: 857-872; Jensen J A, Bjerngaard R. Directional velocityestimation using focusing along the flow direction II: experimentalinvestigation. IEEE Trans. Ultrason. Ferroelec. Freq. Contr., 2003; 50:873-880; Kortbek J, Jensen J A. Estimation of velocity vector anglesusing the directional cross-correlation method. IEEE Trans. Ultrason.Ferroelec Freq. Contr., 2006; 53: 2036-2049). While each of theseapproaches has its own merit, they are all known to yield erroneous flowvector estimates under certain scenarios. Notably, Doppler/phase-shiftestimation is prone to aliasing artifacts when tracking fast flow,whereas speckle tracking and directional cross-correlation havedifficulty in following out-of-plane motion (Hansen L K, Udesen J,Oddershede N, Henze L, Thomsen C, Jensen J A, Nielsen M B. In vivocomparison of three ultrasound vector velocity techniques to MR phasecontrast angiography. Ultrasonics, 2009; 49: 659-667; Swillens A, SegersP, Torp H, Lovstakken L. Two-dimensional blood velocity estimation withultrasound: speckle tracking versus crossed-beam vector Doppler based onflow simulations in a carotid bifurcation model. IEEE Trans. Ultrason.Ferroelec. Freq. Contr., 2010a; 57: 327-339). These frailties areparticularly exposed when flow velocities vary significantly overdifferent phases of a pulsatile flow cycle and when the imaging framerate is inadequate (Swillens A, Segers P, Lovstakken L. Two-dimensionalflow imaging in the carotid bifurcation using a combined speckletracking and phase-shift estimator: a study based on ultrasoundsimulations and in vivo analysis. Ultrasound Med. Biol., 2010b; 36:1722-1735).

SUMMARY OF THE INVENTION

The present invention is directed to an apparatus and methods forimaging and complex analysis of vascular flow with spatiotemporalfluctuations that is non-invasive, accurate, and time-resolved. Inparticular, the invention is a new ultrasound-based framework that canbe called “Vector Projectile Imaging” (VPI), which dynamically renderscomplex flow patterns over an imaging view at millisecond timeresolution. VPI is founded upon three principles: (i) high-frame-ratebroad-view data acquisition (based on steered plane wave firings); (ii)flow vector estimation derived from multi-angle Doppler analysis(coupled with data regularization and least-squares fitting); and (iii)dynamic visualization of color-encoded vector projectiles (with flowspeckles displayed as an adjunct).

VPI can enable quantitative and consistent tracking of spatiotemporallyvarying flow trajectories in curvy vascular geometries like the carotidbifurcation. The present invention is more advanced than currentmethods. In particular, the present invention has duplex mode flowinformation, including velocity-encoded flow projectiles (instead ofjust a particle) and flow speckles. The present invention utilizes newmethods for both data processing and rendering to support consistentflow estimation. In designing VPI, consistent flow vector estimationperformance is achieved through the integrative use of: (i) broad-viewinsonation schemes that can readily offer high data acquisition framerates well beyond the video display range; and (ii) multi-angle Doppleranalysis coupled with post-hoc regularization strategies andleast-squares estimation principles. Furthermore, provided that highimaging frame rates and consistent flow vector estimates are available,it is estimated that dynamic visualization of flow vectors can be madepossible through rendering them in a duplex form that depicts: (i)particle projectiles, which quantitatively highlight the local flowspeed, orientation, and trajectory; and (ii) flow speckles, which serveas a qualitative adjunct to enhance visualization effect.

The present invention is readily distinguished from earlier efforts thatshowed the feasibility of achieving high-frame-rate vector flow imagingthrough spherical wave firings (Nikolov S I, Jensen J A. In-vivosynthetic aperture flow imaging in medical ultrasound. IEEE Trans.Ultrason. Ferroelec. Freq. Contr., 2003; 50: 848-856; Oddershede N,Jensen J A. Effects influencing focusing in synthetic aperture vectorflow imaging. IEEE Trans. Ultrason. Ferroelec. Freq. Contr., 2007; 54:1811-1825) or plane wave excitation (Ekroll I K, Swillens A, Segers P,Dahl T, Torp H, Lovstakken L. Simultaneous quantification of flow andtissue velocities based on multi-angle plane wave imaging. IEEE Trans.Ultrason. Ferroelec. Freq. Contr., 2013; 60: 727-738; Flynn J, Daigle R,Pflugrath L, Linkhart K, Kaczkowski P. Estimation and display for vectorDoppler imaging using plane wave transmissions. Proc. IEEE Ultrason.Symp., 2011; 413-418, Flynn J, Daigle R, Pflugrath L, Kaczkowski P. Highframe rate vector velocity blood flow imaging using a single plane wavetransmission angle. Proc. IEEE Ultrason. Symp., 2012; 323-325; Lu J Y,Wang Z, Kwon S J. Blood flow velocity vector imaging with high framerate imaging methods. Proc. IEEE Ultrason. Symp., 2006; 963-967; UdesenJ, Gran F, Hensen K L, Jensen J A, Thomsen C, Nielsen M B. Highframe-rate blood vector velocity imaging using plane waves: simulationsand preliminary experiments. IEEE Trans. Ultrason. Ferroelec. Freq.Contr., 2008; 55: 1729-1743). As will be demonstrated through ananthropomorphic flow phantom validation study, VPI represents an imaginginnovation that uniquely couples high-frame-rate data acquisition,regularized flow vector estimation, and novelties in dynamicvisualization.

VPI has the following key features that distinguish it from conventionalcolor flow imaging (CFI): 1) Can readily offer imaging frame rates wellbeyond video display range (e.g. >1,000 fps); 2) Provides estimates offlow velocity vectors to account for multi-directional flow components;3) Projectile-based rendering of flow vectors to highlight theirspatiotemporal dynamics. These features are made possible through aunique marriage of broad-view data acquisition principles, flow vectoranalysis algorithms, and novelties in computer vision.

The steps of the technique of the present invention include dataacquisition, regularized flow vector estimation, and dynamicvisualization. Each of the steps can be briefly summarized as follows.

1. Data Acquisition: VPI is based on the use of M steered plane waves¹during ultrasonic transmission (Tx). For each Tx angle, parallelbeam-forming for a 2-D image grid is performed over N dynamic receive(Rx) steering angles. The M-Tx pulsing scheme is looped repeatedly asanalogous to slow-time sampling in Doppler. The effective frame rate forVPI is then simply equal to FR=f_(PW)/M, where f_(PW) is the rate ofeach plane wave firing event (i.e. equal to the pulse repetitionfrequency, or PRF). By simply adjusting PRF, the FR can be boostedto >1,000 fps as needed to track fast-changing flow. Note that, for eachpixel P_(o) within the 2-D image grid, there are MN beam-formedensembles along slow-time (i.e. MN number of 1-D slow-time signalarrays; each corresponding to one combination of Tx-Rx angle).

2. Regularized Flow Vector Estimation: This process is performedindependently for individual pixels. In every realization, the processcan be divided into two stages: (i) velocity estimation for each of theMN slow-time ensembles for that pixel; (ii) vector computation vialeast-squares fitting of MN velocity estimates derived from all Tx-Rxangle pairs. In Stage 1, for each of the MN slow-time ensembles (matrixnotation x_(mn)), multi-level sub-sampling is first performed to attainfiner slow-time resolution. For this set of sub-sampled ensemblesconstructed for x_(mn), three steps are performed: (i) clutter filter(to suppress tissue echoes); (ii) velocity estimation (based on lag-oneautocorrelation: the classical CFI estimator); (iii) aliasingcorrection. After that, the sub-sampled ensembles are averaged to arriveat the mean flow estimate for that Tx-Rx angle pair. After doing thesame for all angle pairs, MN raw velocity values (matrix notation u)would become available. In Stage 2, a flow vector v=(v_(x), v_(z)) isderived from u as follows. First, based on cross-beam Dopplerprinciples² an MN×2 angle matrix A is formed from all MN Tx-Rx anglecombinations. It is known that u=Av. Hence, v is computed by carryingout the least-squares fitting operation Au.

3. Dynamic Visualization: For the v estimate of each pixel, asingle-hue, color-coded arrow is formed. For high velocity magnitude,its corresponding arrow would be brighter in color and longer in length.Arrows for different VPI frames are compiled, and they are displayed asmoving projectiles to enable quantitative visualization.

BRIEF DESCRIPTION OF THE DRAWINGS

This patent or application contains at least one drawing executed incolor. Copies of this patent or patent application publication withcolor drawing(s) will be provided by the Office upon request and paymentof the necessary fee.

FIGS. 1a and 1b illustrate data acquisition in practicing the presentinvention based upon the use of plane wave transmissions and parallelbeam-forming (both performed from multiple angles);

FIGS. 2a and 2b illustrates an arrangement for flow vector estimationaccording to the present invention for every pixel position and itscorresponding set of slow-time signals from all Tx-Rx angle pairs;

FIGS. 3a and 3b are quantitative flow visualizations according to thepresent invention utilizing dynamic rendering of color-encoded particleprojectiles;

FIGS. 4a, 4b and 4c illustrate a set up for an anthropomorphic carotidbifurcation phantom study and an image of the co-planar geometry of acarotid bifurcation of a healthy and a diseased patient, respectively;

FIGS. 5a and 5b illustrate a color static map of estimated flow vectorsand a graph of velocity versus position from the proximal wall of vesselfor vessels at three different depths;

FIGS. 6a-6d are still frame renderings according to the presentinvention showing the formation and dissipation of flow disturbance in ahealthy carotid bifurcation phantom at (a) peak systole; (b) end ofpost-systolic down stroke; (c) dicrotic wave peak; and (d) end ofdicrotic wave, while FIG. 6e shows the relative positions in the pulsecycle in a Doppler spectrogram;

FIGS. 7a-7d illustrate spatiotemporal differences in the twopost-stenotic flow recirculation zones in the carotid bifurcationphantom with 50% ICA eccentric stenosis at: (a) peak systole; (b)arrival of post-systolic jet front at ICA distal end; (c) dicrotic wavepeak; and (d) arrival of post-dicrotic jet front at ICA distal end,while FIG. 7e shows the relative positions in the pulse cycle in aDoppler spectrogram;

FIGS. 8a and 8b illustrate differences in the spatial-peak size of flowrecirculation zones observed (a) after the systole and (b) after thedicrotic wave in the carotid bulb of the healthy bifurcation phantom,while FIG. 8c shows the corresponding instants in two Dopplerspectrograms when these two images occur in the pulse cycle;

FIGS. 9a and 9b show flow recirculation zones in the 50%-stenosedbifurcation phantom during peak systole and dicrotic wave peak, with therelative time marked in two Doppler spectrograms in FIG. 9c ; whileFIGS. 9d and 9e show the recirculation zone adjacent to the ICA innerwall during: (d) the systole; and (e) the dicrotic wave, while FIG. 9fshows he relative time marked in to Doppler spectrograms for two samplevolumes placed at the proximal and distal ends of the ICA inner wall;

FIG. 10 is a system-level schematic of the stages involved in VPIaccording to the present invention;

FIGS. 11a and 11b are images of examples of VPI taken at peak systolefor two carotid bifurcation models: (a) healthy and (b) with 50%eccentric stenosis at the entrance to ICA;

FIGS. 12a to 12d are still frame renderings according to the presentinvention showing only in gray scale speckles the formation anddissipation of flow disturbance in a healthy carotid bifurcation phantomat (a) peak systole; (b) end of post-systolic down stroke; (c) dicroticwave peak; and (d) end of dicrotic wave; and

FIGS. 13a to 13d are still frame renderings according to the presentinvention showing only projectiles in the formation and dissipation offlow disturbance in a healthy carotid bifurcation phantom at (a) peaksystole; (b) end of post-systolic down stroke; (c) dicrotic wave peak;and (d) end of dicrotic wave.

DETAILED DESCRIPTION OF THE INVENTION

An arrangement of apparatus for carrying out the vector projectileimaging (VPI) of the present invention is illustrated in FIG. 10. Thisarrangement carries out the steps of (1) data acquisition, (2)regularized flow vector estimation (including a first stage ofmulti-level sub-sampling and a second stage of flow vector derivation)and (3) dynamic visualization.

To achieve data acquisition an ultrasonic array transducer 10 ispositioned on the outside of the patient's body adjacent the vasculaturein which the fluid (e.g., blood) is to be imaged. The array 10 transmitsa series of ultrasonic unfocused, steered plane waves 11 into the tissueat a high rate. The transmission angle with respect to the transducersurface 13 is changed after each wave. The transducer 10 also receivesthe waves reflected from the tissue at different receive steering anglesand stores it in Pre-beam-Formed Data Acquisition device 12. This datais in the form of frames for each angle.

Each received frame of data is applied to a separate Beam Former 30(enclosed in dotted lines), which includes Beam-Forming circuits 14 ₁ to14 _(N). The output of each beam forming circuit is sub-sampled inSub-Sampling circuits 16 ₁ to 16 _(K) for levels 1 through K. In turn,the output of each sub-sampling circuit is processed in a RegularizedFlow Estimation circuit 18. Then the outputs of the flow estimationcircuits for a frame are averaged in circuits 20.

A Least Squares Vector Estimation circuit 22 performs two majorprocessing stages, i.e., (i) regularizing of the frequency shiftestimation on each frame and; (ii) axial-lateral vector componentestimation based on least-squares fitting. This circuit uses acustomized estimation algorithm with post-hoc data regularization. InDisplay Rendering circuit 24 a duplex visualization method is used inwhich the primary channel shows color-encoded particle projectiles(little arrows) whose color code and length are both related to thevelocity magnitude at a particular location in the imaged vasculature.The direction of the projectiles shows flow direction. The position ofthese projectiles is dynamically updated between frames toquantitatively highlight flow paths together with changes in magnitudeand orientation. The secondary visualization channel depicts grayscaleflow speckles that are derived based on the slow-time filter power. Thissupplementary flow information serves as an adjunct depiction of flowtrajectories. The output of circuit 24 is the VPI image 26

Data Acquisition

Data acquisition in VPI is based upon the use of plane wavetransmissions and parallel beam-forming (both performed from multipleangles). As shown in FIG. 1a , on transmission (Tx), M plane wavepulsing events 11 are fired in sequence, and they each have a differentsteering angle. This group of firings is repeatedly executed tofacilitate slow-time data acquisition. As shown in FIG. 1b , onreception (Rx), parallel beam-forming of N data frames, each with adifferent steering angle, is carried out for every plane wave pulsingevent. The same pulsing sequence comprises MN Tx-Rx angle pairs.

Using a VPI framework, acquisition of flow vector information at highframe rates is facilitated by performing steered plane wavetransmissions whose operating principles have recently matured forultrasound imaging applications. See, Montaldo G, Tanter M, Bercoff J,Benech N, Fink M., “Coherent plane-wave compounding for very high framerate ultrasonography and transient elastography,” IEEE Trans. Ultrason.Ferroelec. Freq. Contr., (2009), 56: 489-506, which is incorporatedherein in its entirety. As shown in FIG. 1a , the firing sequencecomprises a group of M broad-view unfocused pulsing events that aretransmitted in order. Between adjacent firings, the transmission (Tx)steering angle (i.e. the propagation angle with respect to thetransducer surface normal 13) is incrementally changed so as to cover aspan of M angles over the entire group of pulsing events. This dataacquisition scheme can be considered as the generalized form of thetwo-angle plane-wave firing strategy that has been applied to vectorflow estimation (Ekroll et al. 2013 cited above). The merit of usingmore than two Tx angles is that flow vectors can be robustly estimatedby solving an over-determined system of linear equations based onleast-squares fitting principles. For a sequence with M Tx angles andpulse repetition frequency f_(PRF), the nominal data acquisition framerate (f_(DAQ)) (i.e. rate at which one group of firings can be executed)is in effect equal to f_(PRF)/M. Since f_(PRF) is typically in the kHzrange in ultrasound imaging, f_(DAQ) can be well beyond the videodisplay range as long as the number of Tx angles is kept small.

For each plane wave transmission at a given Tx angle, a set of Nbeam-formed data frames is generated in parallel based on thecorresponding array of channel-domain pulse echoes (waves reflected fromthe tissue) which are acquired from the transducer 10 at the Pre-BeamForming Data Acquisition Device 12. As illustrated in FIG. 1b , eachframe is formed with a different receive (Rx) steering angle. Thebeam-formed data value of individual pixel positions in the frame iscomputed by leveraging well-established dynamic receive focusingprinciples that can be executed at real-time throughputs using parallelcomputing solutions. See, Yiu B Y S, Tsang I K H, Yu A C H, “GPU-basedbeam former: fast realization of synthetic aperture imaging and planewave compounding,” IEEE Trans. Ultrason. Ferroelec. Freq. Contr.,(2011), 58: 1698-1705, which is incorporated herein in its entirety? Ingeneral, with M unique Tx angles, beam-formed data frames are derivedfor MN combinations of Tx-Rx angle pairs (see FIG. 1b ). The mainrationale for using multiple Rx angles is that such a strategy wouldeffectively increase the total number of independent frequency shiftestimates (MN instead of M) available for vector flow estimation. Therobustness of the least-squares vector estimation procedure can then befurther enhanced, and in turn, more consistent flow vector estimates canbe derived (to be discussed in the following subsections).

In order to monitor temporal changes in flow dynamics, plane wavetransmission and receive beam-forming are carried out multiple times forall MN Tx-Rx angle pairs (as indicated in FIG. 1a ). This process isessentially the same as performing slow-time sampling in single-gatepulsed Doppler ultrasound as disclosed in Evans D H, McDicken W N.Doppler Ultrasound: Physics, Instrumentation and Signal Processing.2^(nd) Ed. New York: Wiley, (2000), which is incorporated herein in itsentirety. As such, at every pixel position, there are MN (one for eachTx-Rx angle pair) slow-time ensembles of beam-formed samples availablefor flow vector estimation. For all ensembles, the slow-time samplingrate is simply equivalent to f_(DAQ) (i.e. repetition rate for one groupof Tx pulsing events), which in turn is equal to f_(PRF)/M as describedin Bercoff J, Montaldo G, Loupas T, Savery D, Meziere F, Fink M, TanterM., “Ultrafast compound Doppler imaging: providing full blood flowcharacterization,” IEEE Trans. Ultrason. Ferroelec. Freq. Contr.,(2011), 58: 134-147, which is incorporated herein by reference in itsentirety. In turn, the slow-time aliasing limit, which equals 2fDAQaccording to the Nyquist theorem, is given by 2f_(PRF)/M. In cases wherea higher slow-time aliasing limit is needed to facilitate tracking offaster flow velocities, the number of Tx angles should be kept small; aswell, a higher f_(PRF) should be used as long as it satisfies themaximum imaging depth limit, which is after all governed by thepulse-echo sensing relation zmax 5 co/2f_(PRF) (Evans and McDicken 2000cited above).

Flow Vector Estimation

At each slow-time instant, the VPI method of the present inventionperforms flow vector estimation independently at all pixel positionsbased on their corresponding set of MN slow-time ensembles.

Flow vector estimation in VPI works by processing, for every pixelposition, its corresponding set of slow-time signals from all Tx-Rxangle pairs. FIG. 2(a) illustrates clutter filtering and frequency shiftestimation performed individually on each Tx-Rx angle pair in order tocalculate the flow vector (v_(x)[t], v_(z)[t]). Least-squares fitting isthen performed with the set of frequency shift estimates {v_(mn)[t]} asdata input. FIG. 2(b) illustrates that for the m^(th) Tx angle andn^(th) Rx angle, regularized frequency shift estimation involves:autocorrelation computations over a slow-time sliding window (lag-onephase and lag-zero magnitude used respectively for frequency and powercalculation), flow region masking based on determining the powerthreshold, and phase unwrapping.

As illustrated in FIG. 2a , clutter filtering with filters 30 is firstapplied individually to each slow-time ensemble to suppress unwantedtissue echoes or reflections of the transmitted signal. Subsequently,two major processing stages are carried out: (i) regularized slow-timefrequency shift estimation on each of the MN filtered ensembles iscarried out in the estimation circuits 32; and (ii) axial-lateral vectorcomponent estimation based on least-squares fitting of the MN frequencyshift estimates that correspond to different Tx-Rx angle pairs iscarried out in Least-Squares Vector Estimator 22 (shown in FIG. 10). Thespecific operations of each processing stage are described as follows.

To obtain consistent slow-time frequency shift estimates as necessaryfor accurate vector computation, a customized estimation algorithm withpost-hoc data regularization is devised to individually process everyfiltered slow-time ensemble. As shown in FIG. 2b , the algorithm beginsby calculating the mean signal frequency at various slow-time instantsthrough the use of a sliding window strategy. For this step, a slow-timedata window (centered about a given time of interest) is first definedover a filtered ensemble, and then the mean frequency over the windowedsegment is computed using the well-established lag-one autocorrelationphase algorithm in estimator 36. See, Evans 2010 cited above, which isincorporated herein in its entirety. To facilitate flow region detectionand adjunct rendering of flow speckles, the mean filtered power over theslow-time window is also calculated in parallel by finding the lag-zeroautocorrelation magnitude. This estimation process is repeated at otherslow-time instants by simply repositioning the window at the new time ofinterest. In turn, ensembles of slow-time frequency and power estimatesare derived for each of the MN Tx-Rx angle pairs.

Following the estimation steps, a two-stage post-hoc processing strategyis performed to regularize entries of the slow-time frequency estimateensembles. First, to remove spurious estimates at time instants whereflow is not detected by a Tx-Rx angle pair, entries in the slow-timefrequency ensembles are set to zero if their respective slow-time powerestimate at that instant is below a predefined threshold (i.e. a flowclassification mask 38 is applied similar to the color gain mask incolor flow imaging). Second, akin to previous efforts in color flowsignal processing, phase unwrapping is applied to the sifted slow-timefrequency estimates to account for possible aliasing artifacts that maywell occur when performing the lag-one autocorrelation algorithm. See,Lai X, Torp H, Kristoffersen K, “An extended autocorrelation method forestimation of blood velocity,” IEEE Trans. Ultrason. Ferroelec. Freq.Contr., (1997), 44: 1332-1342, which is incorporated herein in itsentirety. This step effectively extends the dynamic range of theslow-time frequency estimates beyond the Nyquist sampling limit. Notethat both regularization steps are performed individually on all MNensembles of slow-time frequency estimates.

Least-Squares Vector Computation Algorithm

Once the MN slow-time frequency shifts are estimated from all Tx-Rxangle pairs, the axial and lateral components of the flow vector arederived using multi-angle Doppler analysis principles. See, Dunmire etal. 2000 cited above, which is incorporated in its entirety. Thiscomputational task is equivalent to solving an over-determined system ofequations whereby MN data values (i.e. frequency shift estimates fromall the Tx-Rx angle pairs at one slow-time instant) are used as inputsto solve for two unknowns (i.e. axial velocity and lateral velocity).Specifically, the flow vector v=(v_(z), v_(x)) can be estimated througha least-squares fitting approach. The advantage of adopting thisalgebraic framework is that each resulting flow vector estimate would beoptimized in the sense that its mean squared error is minimized for agiven input. In turn, in cases with noisy data input, consistentestimation performance can still be maintained compared with thetwo-equation, two-unknown formulation that corresponds to theconventional two-angle vector Doppler method (Ekroll et al. 2013;Kripfgans et al. 2006 cited above).

In the least-squares vector computation method, v can be calculated bycarrying out a matrix operation with each MN×1 measurement vector u(consisting of individual frequency shift values).

The least-squares flow vector estimator can be considered a generalizedform of the cross-beam Doppler estimation method in which multiple Tx-Rxangle pairs are used in lieu of the two-angle approach that has beenreported previously. See, Kripfgans et al. 2006; Tortoli et al. 2006,2010; and Ekroll et al. 2013, all cited above and incorporated herein intheir entirety. In the case with MN combinations of Tx-Rx angle pairs,the m^(th) Tx angle can be denoted as θ_(m) and the n^(th) Rx angle canbe denoted as φ_(n). Note that, since plane wave transmissions anddynamic receive focusing are used, θ_(m) and φ_(n) would remain the samefor all pixels within the imaging view. It is well-known from theDoppler equation that, with this angle pair configuration, the slow-timefrequency shift ϕ_(mn) for an object moving at velocity magnitude v andangle α is equal to:

$\begin{matrix}{{\varphi_{mn} = \; {\frac{{v\; {\cos \left( {\theta_{m\;} - \alpha} \right)}} + {v\; {\cos \left( {\phi_{n} - \alpha} \right)}}}{c_{o}}f_{o}}},} & (1)\end{matrix}$

where c_(o) is the acoustic speed and f_(o) is the ultrasound centerfrequency. See, Dunmire et al. 2000, cited above and incorporated hereinin its entirety. Following similar derivations, the mathematical formexpressed in (A1) can be modified by noting two points: (i) there existsa trigonometry relation [cos(A−B)=cos(A)cos(B)+sin(A)sin(B)]; and (ii)the axial and lateral velocity components are respectively equal tov_(z)=v cos(α) and v_(x)=v sin(α). See, Tsang I K H, Yiu B Y S, Yu A CH, “A least-squares vector flow estimator for synthetic apertureimaging,” Proc. IEEE Ultrason. Symp., (2009), 1387-1390, which isincorporated herein in its entirety. Substituting these relations into(A1), the following revised form of the Doppler equation can beobtained:

$\begin{matrix}{{{v_{z}\left( {{\cos \; \theta_{m}} + {\cos \; \phi_{n}}} \right)} + {v_{x}\left( {{\sin \; \theta_{m}} + {\sin \; \phi_{n}}} \right)}} = {\frac{c_{o}}{f_{o}}{\varphi_{mn}.}}} & (2)\end{matrix}$

The flow vector estimator seeks to solve for v_(x) and v_(z), the twounknowns in (A2), by forming an over-determined system of equations fromMN realizations of (A2) as made available through the use of differentTx-Rx angle pairs. In matrix notation, this system of equations can beexpressed in the following form for a given flow vector v=(v_(x),v_(z)):

$\begin{matrix}{{Av}\; = \; {\left. u\;\Rightarrow{\begin{bmatrix}{{\cos \; \theta_{1}} + \; {\cos \; \phi_{1}}} & {{\sin \; \theta_{1}} + \; {\sin \; \phi_{1}}} \\\vdots & \vdots \\{{\cos \; \theta_{M}} + \; {\cos \; \phi_{N}}} & {{\sin \; \theta_{M}} + \; {\sin \; \phi_{N}}}\end{bmatrix}\begin{bmatrix}v_{z} \\v_{x}\end{bmatrix}} \right. = \begin{bmatrix}u_{11} \\\vdots \\u_{MN}\end{bmatrix}}} & (3)\end{matrix}$

where A is the angle-pair matrix (MN×2 in size) and u as the measurementvector (MN×1 in size). Note that u_(mn) is essentially equal to theright hand side of (A2) for a given Tx-Rx angle pair (i.e.u_(mn)=c_(o)ϕ_(mn)/f_(o)).

From linear algebra principles, it is well known that v in Equation (3)can be found by multiplying the pseudo-inverse of A with v: a solutionthat is often referred to as the least-squares fitting solution. See,Moon T K, Stirling W C, “Mathematical Methods and Algorithms for SignalProcessing,” Upper Saddle River: Prentice-Hall, (2000), which isincorporated herein in its entirety. Thus, with each MN×1 measurementvector u (consisting of individual frequency shift values), v can becalculated by carrying out the following matrix operation:

$\begin{matrix}{v = {\begin{bmatrix}v_{z} \\v_{x}\end{bmatrix} = {\left( {A^{T}A} \right)^{- 1}A^{T}u}}} & (4)\end{matrix}$

where the T superscript denotes a matrix transpose operation and entity(A^(T)A)⁻¹A^(T) is well-known in linear algebra as the pseudo-inverse ofmatrix A. See Moon T K, Stirling W C, “Mathematical Methods andAlgorithms for Signal Processing,” Upper Saddle River: Prentice-Hall,(2000), which is incorporated herein in its entirety. Note that thepseudo-inverse (A^(T)A)⁻¹A^(T) is essentially a 2×MN matrix of constantvalues (as long as the Tx-Rx angle pairs remain the same). Thus, thesame pseudo-inverse is applicable to different pixel positions. It isalso worth pointing out that, for the least-squares estimator given inEquation (4), the resulting flow vector estimate can be considered as anoptimal solution in the sense that its mean-squared error is minimizedfor a given input. It is worth emphasizing that Equation (4) is carriedout individually at every pixel position and at each slow-time instant.

Dynamic Visualization Procedure

Using the computation protocol according to the present invention,frames of flow vector information can be generated at a rate of f_(VPI),which equals to f_(DAQ)/K [i.e. f_(PRF)/(MK)] for a step size of Kslow-time samples when executing the sliding window implementation. Tofacilitate dynamic rendering of these flow vector estimates, a novelduplex visualization method is used. Its primary visualization channelshows color-encoded particle projectiles (small arrows) whose color codeand projectile length are both related to the velocity magnitude (on ascale from zero to a tunable maximum value). The direction of theprojectiles shows flow direction. The position of these projectiles isdynamically updated between frames to quantitatively highlight flowpaths together with changes in magnitude and orientation. The secondaryvisualization channel depicts grayscale flow speckles that are derivedbased on the slow-time filter power. This supplementary flow informationserves as an adjunct depiction of flow trajectories in ways similar tothat offered by the B-flow imaging technique. See, Chiao R Y, Mo L Y,Hall A L, Miller S C, Thomenius K E, “B-mode blood flow (B-flow)imaging,” In: Proceedings, IEEE Ultrasonics Symposium, San Juan, PuertoRico, 22-25 October. New York: IEEE; (2000), p. 1469-1472; andLovstakken L, Bjaerum S, Martens D, Torp H, “Blood flow imaging—A newreal-time, 2-D flow imaging technique,” IEEE Trans Ultrason FerroelectrFreq Control (2006),53:289-299. Note that the graphical representationof multidirectional flow dynamics rendered by our duplex visualizationapproach is essentially different from the dot-based particlevisualization algorithm that has been reported recently in ultrasoundflow imaging (Flynn et al. 2011).

VPI provides quantitative flow visualization through dynamic renderingof color-encoded particle projectiles. In FIG. 3(a) a set of pixels inthe image view is first designated as projectile launch points. Thoseoutside the flow region (identified based on power thresholds) arehidden. Projectile length and color hue are set based on velocitymagnitude. FIG. 3(b) shows the projectile position updated bycalculating its inter-frame displacement based on the velocity vectorestimate.

The dynamic projectile method of the VPI visualization protocol works asfollows: First, as shown in FIG. 3a , at the start of the loop, a randomset of pixels in the imaging view are chosen as launch points, and theirrespective color-encoded projectiles are displayed. Subsequently, toupdate each projectile's position in the next frame, three steps areexecuted in sequence as shown in FIG. 3b : (i) calculating theincremental 2-D displacement by multiplying between the projectile'scorresponding axial-lateral velocities and the inter-frame period (i.e.reciprocal of f_(VPI)); (ii) updating the projectile's position in thenew frame based on the calculated displacement (discretized to thenearest pixel in the image grid); and (iii) displaying the color-encodedprojectile of the new frame at the updated position. This process isessentially similar to algorithms proposed in the computer graphicsfield and is repeated for a given projectile lifetime (randomized interms of the number of frames), and afterward the entire dynamicvisualization loop is restarted by regenerating new projectiles at thelaunch points (based on vector estimates at the new slow-time instant).See, McLoughlin T, Laramee R S, Peikert R, Post F H, Chen M, “Over twodecades of integration-based, geometric flow visualization,” ComputerGraphics Forum 2010; 29:1807-1829. Note that, to suppress spuriousprojectiles, a display gain strategy is adopted as similar to that usedin color flow imaging. In particular, a projectile would be displayedonly if its instantaneous pixel position falls within the flow region,as identified based on the slow-time filtered power map (i.e. pixelswith power greater than a given threshold are classified as flowregion). Otherwise, a new projectile would be regenerated at theoriginal launch point.

Hardware and Parameters

The VPI invention has been implemented using a research-purpose,channel-domain imaging platform that allows the transmission andreception operations of each array element to be configuredindividually. This platform is a composite system in which the front-endof a SonixTouch research scanner (Ultrasonix, Richmond, BC, Canada) wascoupled to a pre-beam-formed data acquisition tool, and data wasstreamed to a back-end computing workstation through a universal serialbus link (specifications listed in Table 1a). An L14-5 linear array(Ultrasonix) was used as the operating transducer. See, Cheung C C P, YuA C H, Salimi N, Yiu B Y S, Tsang I K H, Kirby B, Azar R Z, Dickie K,“Multi-channel pre-beamform data acquisition system for research onadvanced ultrasound imaging methods,” IEEE Trans. Ultrason. Ferroelec.Freq. Contr., (2012) 59: 243-253, which is incorporated herein in itsentirety.

Pressure field recordings of this ultrasound transmission hardware weretaken using a membrane hydrophone (HMB-0500, Onda, Sunnyvale, Calif.,USA) that was mounted on a three-axis micro-positioner (ASTS-01, Onda).When operating in plane wave excitation mode, our scanner hardwaregenerated a derated peak negative pressure of 0.72 MPa (located at 2-cmdepth). This pressure value, for our given pulsing parameters,corresponded to a mechanical index of 0.32; spatial-peak,temporal-average intensity of 0.16 W/cm2; and spatial-peak,temporal-peak intensity of 27 W/cm2 (assuming operation in 37_C degassedwater). These numbers were well within the safety limits defined by theU.S. Food and Drugs Administration. See Duck F A, “Medical andnon-medical protection standards for ultrasound and infrasound,” ProgBiophys Mol Biol (2007) 93: 176-191.

A vector estimation configuration with three Tx angles (−10°, 0°, +10°)and three Rx angles (−10°, 0°, +10°) was implemented (i.e. M=3, N=3,MN=9). To realize such a configuration, a steered plane wave pulsingsequence was programmed on the platform by executing relevant functionsin the TEXO software development kit (Ultrasonix) to define arraychannel delays that only generate angle steering without focusing.Typical pulse-echo imaging parameters were used as summarized in Table1b, and pre-beam-formed channel-domain data was acquired on reception.

TABLE 1 Parameters Used for Experimental Realization of VPI ParameterValue (a) Imaging Platform Number of Tx/Rx Channels 128 Array Pitch0.3048 mm Pre-Beam formed Data Sampling Rate 40 MHz Pre-Beam formed DataBit Resolution  12 (b) Data Acquisition Imaging Frequency 5 MHz Tx PulseDuration 3 cycles (0.6 μs) Pulse Repetition Frequency 10 kHz EffectiveData Acquisition Rate 3.33 kHz Maximum Imaging Depth 2 cm DataAcquisition Duration 1 s (c) Beam Forming Pre-Beam-formed Data FilterPass band 3-7 MHz Filter Design Method Equiripple Data Frame Size 200 ×380 pixels Pixel Dimension 0.1 × 0.1 mm (d) Slow-time data processingNormalized clutter filter cutoff  0.05 Sliding Window for flowestimation 128 samples Sliding Window Step Size 8 samples (d) VPIVisualization Nominal Frame Rate 416 fps Launch Point Density 4% MeanProjectile Lifetime 30 frames Flow Speckle Dynamic Range 40 dB

TABLE 2 Alternative Experimental Parameters Parameter Value ImagingSpecifications Imaging frequency 5 MHz # of array channels 128 Pulseduration 3 cycles (0.429 μs) Pulse repetition 10 kHz frequency Tx-Rxsteering angles −10°, 0°, +10° Flow Pattern Specifications Peak inletflow rate 6 ml/s Pulse cycle frequency 1.2 Hz

A 3-Tx, 3-Rx VPI configuration was implemented. Also, for each Tx-Rxangle pair, a 3-level sub-sampling was imposed during flow estimation.VPI was tested on anatomically realistic flow models that resembledhealthy and stenosed carotid bifurcation. These are suitable geometriesbecause flow dynamics within them are known to be multi-directional andsignificantly time-varying. The phantoms are wall-less designs based onlost-core casting with polyvinyl alcohol gel. Pulsatile flow is suppliedthrough the use of a gear pump with programmable flow rates. Theresulting images are shown in FIG. 11. In FIG. 11, the images are of VPItaken at peak systole for two carotid bifurcation models: FIG. 11(a)healthy and FIG. 11(b) with 50% eccentric stenosis at the entrance toICA. This shows examples of VPI in rendering long-axis views of twobifurcation models. The results at peak systole are shown. In thehealthy case, VPI accurately projected the main transit path of bloodflow. In the stenosis case, VPI quantitatively highlighted the highvelocity jet emerging at the stenosis site, curvy transit pathdownstream from the stenosis, and significant re-circulatory flow in theICA bulb.

After streaming the acquired data offline to the back-end processor,various image formation and visualization operations were carried out asrequired for VPI. First, to improve the channel-domain signal-to-noiseratio, a finite-impulse-response band pass filter (minimum order;parameters listed in Table 1c) was applied to the pre-beam-formed dataof each channel using Matlab (R2012a; Mathworks, Natick, Mass., USA).After that, delay-and-sum beam-forming from the three Rx angles wereexecuted using a graphical processing unit (GPU) based parallelcomputing approach like that disclosed in Yiu et al. 2011, which waspreviously cited and is incorporated by reference in its entirety. Notethat an array of two GTX-590 GPUs (NVidia, Santa Clara, Calif., USA) wasused for this operation to facilitate processing at real-timethroughput. Subsequently, an implementation for speckle imaging was usedas disclosed in Yiu B Y S, Tsang I K H, Yu A C H, “GPU-based beamformer: fast realization of synthetic aperture imaging and plane wavecompounding,” IEEE Trans. Ultrason. Ferroelec. Freq. Contr., (2011), 58:1698-1705. In addition, clutter filtering (in the form of a minimumorder high-pass finite-impulse-response filter; see Table 1d forparameters) and lag-one autocorrelation were performed individually onthe nine Tx-Rx angle pairs at each pixel position. Other downstreamoperations related to vector estimation (post-hoc regularization andleast-squares fitting) were then conducted in Matlab. Ad hoc persistenceand median filtering were also performed. At last, VPI image sets wereobtained and rendered using the duplex dynamic visualization algorithmof the present invention and the parameters listed in Table 1d. Notethat the flow information in our VPI image sets was overlaid on top of abackground B-mode image frame that was formed from spatial compoundingof the beam-formed data frames formed from the nine Tx-Rx angle pairs.

In order to evaluate the accuracy of the flow vector estimationalgorithm used in our VPI technique, steady-flow calibration experimentswere first conducted using a multi-vessel flow phantom that wefabricated in-house. The phantom comprised three wall-less straighttubes whose long axes were aligned along the same plane; each tube had adifferent diameter (2, 4 and 6 mm) and flow angle (−10°, 0° and +10°),and they were positioned at different depths (1.5, 4 and 6 cm). By useof an investment casting protocol similar to that described in ourprevious work (Yiu and Yu 2013, previously cited), the phantom wasfabricated with polyvinyl alcohol cryogel as the tissue-mimickingmaterial, whose acoustic attenuation coefficient and acoustic speed wererespectively measured to be 0.24 dB/cm, MHz and 1518 m/s.

The phantom was connected to a gear pump (AccuFlow-Q, Shelley MedicalImaging, London, ON, Canada) that supplied continuous circulation ofblood-mimicking fluid (Shelley; 1037 kg/m3 density, 3.95 3 106 m2/sviscosity) at a flow rate of 2.5 mL/s. The transducer scan plane wasaligned to the long axis of the three vessels (which were expanded todiameters of 2.2, 4.4 and 6.3, respectively, because of flow-mediateddilation). Raw data were then acquired for the three-Tx, three-Rxconfiguration based on the parameters described above, and the lumenvelocity profiles were estimated using VPI's flow vector computationalgorithm. Results were correlated with the theoretical parabolicprofiles, whose centerline velocities were 131, 31 and 16 cm/s,respectively, for the three dilated vessels

To assess the practical efficacy of the VPI technique, this frameworkwas used to image complex flow dynamics inside anatomically realisticcarotid bifurcation phantoms. In particular, efficacy of VPI wasevaluated through an anthropomorphic carotid bifurcation phantom study.FIG. 4(a) illustrates the experimental setup comprising the flow circuitand the imaging platform. Sample B-mode images are shown for twobifurcation models. In FIG. 4(a) a transmit pulse circuit 40 deliversits signal to the array transducer 10, which is the same or similar tothe one shown in FIG. 10 and which may have, e.g., 128 TX/RX channels.It is triggered by a signal from channel domain data acquisition tool48. The transducer causes ultrasonic waves to be applied to artificialtissue 42, which has a fluid flow path that branches. The fluid from thetissue mimic 42 passes from both branches into a fluid reservoir 44where it is collected and returned to the tissue mimic via a pump 46.The return signal from the tissue mimic 42 is received by the array 10and is delivered to the channel-domain data acquisition tool 48, whichconditions it. Circuit 48 is similar to circuit 12 in FIG. 10. Thisconditioned signal is applied to Beam Former 30, which is the same orsimilar to circuit 30 in FIG. 10. Least squares vector estimation isperformed in circuit 22 and the result is presented on display 26, againin a form similar to that in FIG. 10.

FIG. 4(b) shows the image for a healthy co-planar geometry and FIG. 4(c)shows the image for a diseased bifurcation with 50% eccentric stenosisat the ICA branch entrance. Vessel dimensions are as shown. (CCA=commoncarotid artery; ICA=internal carotid artery; ECA=external carotidartery).

Note that the carotid bifurcation vasculature is rather suitable forthis investigation because it possessed curved vessel geometries in thevicinity of the junction between three branches: the common carotidartery (CCA), the internal carotid artery (ICA), and the externalcarotid artery (ECA). In other words, it effectively allowed testing ofthe ability of the three-Tx, three-Rx VPI configuration to track flowpatterns with significant multi-directional and spatiotemporalvariations. Another point of merit in using these geometries is thattheir flow dynamics have already been extensively characterized byothers using optical particle image velocimetry (Kefayati S, Poepping TL “Transitional flow analysis in the carotid artery bifurcation byproper orthogonal decomposition and particle image velocimetry.” Med.Eng. Phys., 2013; 35: 898-909.; Poepping et al. (2010)) andcomputational fluid dynamics (Steinman D A, Poepping T L, Tambasco M,Rankin R N, Holdsworth D W, “Flow patterns at the stenosed carotidbifurcation: effect of concentric versus eccentric stenosis,” Ann.Biomed. Eng., 2000; 28: 415-423. This information effectively providesan established reference for comparison with the flow patterns renderedby VPI.

Two different carotid bifurcation phantom models were used forexperimentation (i) healthy co-planar geometry (FIG. 4b ) and (ii)diseased bifurcation with 50% eccentric stenosis at the ICA branchentrance (FIG. 4c ). The phantoms were wall-less designs with polyvinylalcohol cryogel as the tissue mimicking material, and they werefabricated using the same procedure as described. See, Yiu and Yu 2013previously cited. The flow pulse, with a 72-bpm pulse rate (i.e., 1.2Hz) and a 5 mL/s systolic flow rate, resembled a carotid pulse patternthat featured a primary systolic upstroke and a secondary dicrotic wave(predefined in the pump system). As explained elsewhere (Yiu and Yu2013), these flow parameters would generally yield laminar flowconditions, and thus any complex flow patterns that arise can beascribed to flow disturbance brought about by local tortuousness in thevessel geometry (rather than flow turbulence).

A steady-flow calibration experiment was first conducted by connectingthe healthy bifurcation phantom to a gear pump (AccuFlow-Q; ShelleyMedical Imaging, London, ON, Canada) that supplied continuouscirculation of blood mimicking fluid (Shelley; 1037 kg/m³ density,3.95×10⁶ m²/s viscosity) at 5 ml/s flow rate. The transducer scan planewas aligned to the CCA long axis (expanded to 6.4 mm diameter due toflow-mediated dilation), and raw data was acquired for the three-Tx,three-Rx configuration based on the parameters described earlier. Thelumen velocity profile was then estimated using VPI's flow vectorcomputation algorithm. Results were compared to the theoreticalparabolic profile (with 31 cm/s centreline velocity).

Next, pulsatile flow experiments were performed using the bifurcationphantoms. The flow pulse, with a 72 bpm pulse rate (i.e. 1.2 Hz) and a 5ml/s systolic flow rate, resembled a carotid pulse pattern that featureda primary systolic upstroke and a secondary dicrotic wave (pre-definedin the pump system). VPI cineloops were then generated by processing rawdata acquired under such flow settings to determine the ability of VPIin visualizing complex flow features. To facilitate comparison, Dopplerspectrograms were computed at representative pixel positions in theimaging view by reprocessing the raw slow-time ensembles at thoseplaces.

The vector computation algorithm of VPI was found to be capable ofderiving flow vector estimates at high accuracy. Corresponding resultsobtained from the steady-flow calibration experiment are shown in FIG.5. FIG. 5 shows the flow vector estimator of vector projectile imaging(VPI) (three-transmission [Tx], three-reception [Rx] configuration)derived consistent accurate flow estimates in a multi-vessel steady-flowcalibration experiment (2.5 mL/s flow rate). FIG. 5(a) shows a staticmap of estimated flow vectors in three flow tubes positioned atdifferent depths (1.5, 4, 6 cm), of different sizes (2, 4, 6 mmdiameter) and oriented at different angles (−10°, 0°, +10°. The colorcode and length of each vector were related to the flow velocitymagnitude. The scale is displayed in log form in view of the highvelocity dynamic range). See FIGS. 5(b)-5(d). For the three vessels, theestimated velocity magnitudes (solid lines) at different axial positionswithin the lumen closely match theory (dashed line). Results averagedfrom 50 lateral positions (error bars 5 standard deviations).

The plots are the flow vector profiles in the CCA of a healthybifurcation phantom (with 5 ml/s constant flow rate) with the transducerplaced in parallel with the CCA vessel. As can be observed in FIG. 5a ,the angle orientation of the flow vectors within the lumen (visualizedas static color-encoded projectiles) was generally accurate in that theyconsistently depicted the flow direction in this calibration flowscenario that comprised three vessels of different angles. The flowangle estimates remained robust at axial positions near the transducer(top vessel, centered at 1.5 cm depth) and away from the transducer(bottom vessel; centered at 6-cm depth).

The estimated flow speed magnitude across the lumen of the three vesselswas generally found to resemble a parabolic shape that matched well withthe theoretical prediction. As illustrated in FIGS. 5(b)-5(d), for thetop, middle and bottom vessels, the estimated centerline velocitymagnitude was respectively 110.4, 28.6 and 15.1 cm/s (each based onaverage of 50 estimates). They were −16.1%, −9.1% and −6.2% differentfrom the theoretical value. This offset is after all typical for meanvelocity estimation, because each spatial point, being a finite-sizedrange gate, actually covered a range of velocities along the parabolicflow gradient, and in turn, the mean velocity estimate would correspondto the average over this depth range.

Calibration results showed that, using three transmit angles and threereceive angles (−10°, 0°, +10° for both), VPI can accurately computeflow vectors even when the transducer was placed in parallel to thevessel (6.4 mm dilated diameter; 5 ml/s steady flow rate). The practicalmerit of VPI was further demonstrated through an anthropomorphic flowphantom investigation that considered both healthy and stenosed carotidbifurcation geometries. For the healthy bifurcation with 1.2 Hz carotidflow pulses, VPI was able to render multi-directional andspatiotemporally varying flow patterns (using 416 fps nominal framerate, or 2.4 ms time resolution). In the case of stenosed bifurcation(50% eccentric narrowing), VPI enabled dynamic visualization ofhigh-speed flow jet and recirculation zones.

Using the VPI technique, time-resolved quantitative visualization ofmulti-directional and spatiotemporally varying flow patterns that emergewithin curvy vasculature under pulsatile flow conditions were achievedfor a healthy carotid bifurcation with 72 bpm pulse rate. As anillustration, FIG. 6 shows the long-axis view of the flow dynamicsinside a healthy carotid bifurcation phantom. In particular FIGS.6(a)-6(d) are still frame VPI renderings showing the formation anddissipation of a flow disturbance in a healthy carotid bifurcationphantom. Frames for four time points are shown, i.e., FIG. 6(a) is forpeak systole; FIG. 6(b) shows the end of the post-systolic down stroke;FIG. 6(c) is the dicrotic wave peak; and FIG. 6(d) shows the end ofdicrotic wave. The relative positions in the pulse cycle are marked inthe Doppler spectrogram shown in FIG. 6(e), which was obtained from a1×1 mm sample volume placed at the CCA center. The nominal VPI framerate (f_(VPI)) and the playback rate were 416 fps and 50 fps,respectively (generated from f_(DAQ) of 3,333 Hz for a three-Tx,three-Rx VPI configuration). Multi-directional and spatiotemporalvariations in the flow pattern are coherently depicted. Also rendered isthe flow disturbance 60 in the ICA carotid bulb.

The nominal VPI frame rate (f_(VPI)) was 416 fps, and it was played backat 50 fps (f_(DAQ) was 3,333 Hz). The rendered flow dynamics were foundto be consistent with well-established findings obtained fromcomputational predictions See, Berger S A, Jou L D, “Flows in stenoticvessels,” Annu. Rev. Fluid Mech., (2000) 32: 347-382). In particular, itcan be readily observed that the temporal evolution of flow speed andflow direction rendered by VPI in different parts of the vasculatureare, as expected, synchronized with the stroke of the flow pulse. Also,in the ECA branch (lower branch), streamlined forward flow (withoutreversal) along the vasculature was evident throughout the pulse cycle.This latter observation effectively demonstrates that VPI's flow vectorestimation procedure is robust against flow angle variations, which doarise in the ECA as its inlet segment is inherently tortuous.

The technical merit of VPI is perhaps more notably demonstrated by itsrendering of flow disturbances in the ICA branch of the healthy carotidbifurcation. This branch corresponds to the upper branch in FIG. 6. Asvisualized, while flow remained laminar on the inner wall side of theICA sinus, the flow pattern on its outer wall side (where the carotidbulb is located) exhibited recirculation behaviour as highlighted byVPI's vortical projectile motion at 60. Such a flow disturbancephenomenon was found to be transitory in nature. In particular, it onlyemerged in certain phases of the pulse cycle.

The millisecond time resolution (2.4 ms for 416 fps nominal frame rate)of VPI effectively enabled tracking of when a flow disturbance emergedin the carotid bulb of the healthy bifurcation vasculature. FIG. 6 showsa series of key VPI frames that representatively depict thistime-varying flow disturbance trend (the corresponding pulse cycle phaseof each frame is marked on the pulsed Doppler spectrogram of the CCAshown in FIG. 6(e). During peak systole (FIG. 6(a)), flow in the carotidbulb region was in the forward direction. However, in the post-systolicdown stroke phase (FIG. 6(b)), a flow recirculation zone A appeared inthis part of the ICA sinus. It subsequently dissipated during thedicrotic wave that produced a secondary flow upstroke (FIG. 6(c)), andflow was again moving forward in this phase of the pulse cycle. At theconclusion of the dicrotic wave, which was preceded by a secondary downstroke, vortical flow B emerged once more (FIG. 6(d)).

To further demonstrate VPI's efficacy in accurately visualizing highlycomplex flow dynamics, FIG. 7 shows still frames of a VPI cineloop ofthe long-axis view of a diseased carotid bifurcation phantom with 50%eccentric stenosis at the entrance to the ICA branch (obtained usingsame imaging parameters as before). In particular, FIG. 7 revealsspatiotemporal differences in the two post-stenotic flow recirculationzones in the carotid bifurcation phantom with 50% ICA eccentricstenosis. The trend is highlighted by VPI frames at four instants: FIG.7(a) peak systole; FIG. 7(b) arrival of post-systolic jet front at ICAdistal end; FIG. 7(c) dicrotic wave peak; and FIG. 7(d) arrival ofpost-dicrotic jet front at ICA distal end. Reference times are marked inFIG. 7(e) that shows the Doppler spectrogram for a range gate at the CCAcenter (1×1 mm sample volume size). VPI can effectively highlighthigh-speed flow jet and flow recirculation zones in a diseased carotidbifurcation phantom with 50% eccentric stenosis at ICA inlet (long-axisview). Imaging parameters are the same as for FIG. 6 (f_(VPI): 416 fps;playback rate: 50 fps). Time-course dynamics of flow disturbance in thetwo recirculation zones are shown in greater detail in the two enlargedwindows.

One striking observation to be noted is that, during systolic upstroke,the formation of a high-velocity flow jet (red arrows) can bedynamically visualized at the site of stenosis. Indeed, the flow jetcontinued to propagate along the inner wall side of the ICA sinus (i.e.the unstenosed side) and spurted across the ICA lumen. It then collidedagainst the outer ICA wall near the distal end of the carotid bulb wherethe ICA vessel started to become straightened. Upon hitting the outerwall, the jet direction was reoriented tangentially against the wall andeventually ramped off before it dissipated further downstream.

In FIG. 7, another key feature visualized by VPI is the presence of twoflow recirculation zones on the two flanks of the post-stenotic flow jetwhich traversed across the ICA lumen. One of the zones was located inthe carotid bulb region C, while the other D was along the inner wallsegment immediately below the curvature of the dissipating flow jetafter it ramped off the outer wall. This observation is in close matchwith the findings derived from flow simulation studies (Steinman et al.2000) and particle image velocimetry experiments (Kefayati and Poepping2013; cited above and Poepping T L, Rankin R N, Holdsworth D W, “Flowpatterns in carotid bifurcation models using pulsed Doppler ultrasound:effect of concentric vs. eccentric stenosis on turbulence andrecirculation,” Ultrasound Med. Biol., (2010) 36: 1125-1134.).

As illustrated in FIG. 7, which shows the four representative VPI framesof the stenosed bifurcation phantom, the two recirculation zones werefound to distinctly differ in spatiotemporal characteristics. For theone at the carotid bulb C, the vortical spin is sustained over theentire pulse cycle without dissolution. In contrast, the flowrecirculation zone D at the inner wall segment had formed and shed twicewithin the same cycle, and it emerged when surrounded by a flow jet archwhich created a substantial fluidic shear force due to the high velocitygradient at the zone boundary. Note that such an arch was not formedwhen the primary and secondary flow jets initially emerged at the siteof stenosis respectively during peak systole (FIG. 7(a 0) and at thedicrotic wave peak (FIG. 7(c)). It only appeared after the jet front hadcompleted its propagation from the stenosis site to the distal end ofthe ICA, thereby encircling the slow-flow components adjacent to theinner wall (FIGS. 7(b) and 7(d)).

Using ultrasound to visualize complex flow dynamics is inherently not astraightforward task. In developing a prospective solution, twopractical vascular flow conditions must be taken into account: (i) at agiven time instant, flow speed and direction (i.e. the flow vector) mayvary spatially because of the tortuous nature of vascular geometry; and(ii) over a cardiac pulse cycle, flow components would deviatetemporally due to pulsatile behaviour. VPI has been designed to captureand render these spatiotemporal dynamics in blood flow.

From a technical standpoint, VPI is equipped with three key featuresthat enable time-resolved visualization of flow vectors over an imagingview. First, it performs high-frame-rate broad-view data acquisition viamulti-angle plane wave imaging principles, so as to achieve the hightime resolution required to monitor flow pulsations and their spatialvariations over an imaging view (FIG. 1). Second, VPI uses a customizedmulti-Tx, multi-Rx Doppler analysis framework to calculate flow vectorsat different pixel positions and at each time instant (FIG. 2); robustestimation performance is attained by incorporating post-hocregularization (flow region detection, phase unwrapping) andleast-squares fitting principles during flow vector computation. Third,VPI dynamically renders flow vectors in the form of color-encodedparticle projectiles whose trajectory is depicted through inter-frameupdates of projectile position (FIG. 3). Dynamic flow perception isenhanced through adjunct display of grayscale flow speckles.

The practical merit of VPI in visualizing complex flow dynamics isdemonstrated through a carotid bifurcation phantom study with controlledflow conditions that are otherwise not possible in-vivo (FIG. 4). In thecase of healthy bifurcation geometry, not only is VPI capable ofaccurately tracking pulsatile streamlined flow (FIG. 6), it also depictsthe transient presence of flow recirculation in the carotid bulb duringthe primary and secondary down stroke phases of the carotid pulse cycle(FIG. 6). The visualization performance of VPI is even more clearly madeevident in the carotid bifurcation geometry with 50% eccentric stenosis.In particular, this new technique effectively highlighted the high-speedflow jet emerging from the stenosis site and its trajectory (FIG. 7).Also, it enabled time-resolved observation of the flow disturbance zonesin the carotid bulb region and along the ICA inner wall segment (FIG.7), both of which were known characteristics of stenosed ICA branches(Kefayati and Poepping 2013; Poepping et al. 2010). The presentinvention is the first in which such complex flow features are beingimaged via ultrasound-based techniques.

As an integrative insight into VPI's application potential indelineating specific details of complex flow patterns, FIG. 8 summarizesthe flow disturbance trends in the healthy carotid bifurcation phantomas observed by this imaging framework. FIGS. 8(a) and 8(b) show twoenlarged views of the ICA which demonstrate VPI's ability to resolvecomplex flow details. Two frames are shown here to depict differences inthe spatial-peak size of flow recirculation zones observed in FIG. 8(a)after systole and FIG. 8(b) after dicrotic wave in the carotid bulb ofthe healthy bifurcation phantom. The corresponding instants of these twoframes in the pulse cycle are labeled in the two Doppler spectrogramsshown in FIG. 8(c), which are extracted from 1×1 mm sample volumesrespectively in the proximal and distal ends of the carotid bulb[position marked by yellow boxes in FIGS. 8(a), 8(b)].

In the case of healthy bifurcation, it should be noted that therecirculation zone in the carotid bulb region is larger at the end ofpost-systolic down stroke (FIG. 8a ) in comparison to that at the end ofdicrotic wave (FIG. 8b ). In particular, as marked in these two frames(white dashed line; drawn based on manual inspection), the zone boundarywas spanned over the entire carotid bulb region during the post-systolicdown stroke phase likely because of the rapid flow deceleration, whereasat the end of the dicrotic wave, the recirculation zone only emerged inthe region proximal to the ICA inlet given the gentler down stroke. Thisvisualization matches well with the Doppler spectrograms (FIG. 8(c))extracted from ranged gates at the proximal and distal ends of thecarotid bulb, where quad-phasic and tri-phasic flow were observedrespectively.

FIG. 9 shows VPI-guided analysis of spatiotemporal characteristics offlow recirculation zones in the 50%-stenosed bifurcation phantom. Inparticular, FIGS. 9(a) and FIG. 9(b) respectively show recirculationpatterns in the carotid bulb during peak systole and dicrotic wave peak.The relative time instant of these two frames is marked in the twoDoppler spectrograms shown in FIG. 9(c), which are taken from the flowjet and the distal end of carotid bulb [yellow boxes in FIGS. 9(a) and9(b)]. For the recirculation zone adjacent to the ICA inner wall, itsspatial-peak size is highlighted by two VPI frames taken during: systoleFIG. 9(d); dicrotic wave FIG. 9(d). For reference, Doppler spectrogramsare shown in FIG. 9(f) for two sample volumes placed at the proximal anddistal ends of the ICA inner wall.

For the stenosed carotid bifurcation, the spatial extent of its two flowrecirculation zones shows substantial differences. While VPI did notdetect significant changes in the size of the carotid bulb recirculationzone over the pulse cycle (FIGS. 9(a) and 9(b)), this new imaging tooldid reveal size variations for the flow recirculation zone at the ICAinner wall (FIGS. 9(d) and 9(e)). Specifically, the primary flow jetarch produced during systole was found to generate a larger flowrecirculation zone along ICA inner wall, whereas the secondary archarising from the dicrotic wave only created a smaller one likely becausethe fluidic shear force was smaller due to the slower jet speed. Such afinding can be confirmed by the Doppler spectrograms (FIG. 9(f))obtained from range gates placed adjacent to the proximal and distalsections of the ICA inner wall where the temporal flow profiles wererespectively quad-phasic and tri-phasic in nature. In contrast, for arange gate placed within the carotid bulb recirculation zone, itsDoppler spectrogram was found to be monophasic and was reciprocal inappearance with respect to that for a range gate placed in the flow jetregion (FIG. 9(c)).

As mentioned above, the adjunct display of grayscale flow speckles canenhance the flow visualization performance of the algorithm becauseinter-frame flow speckle displacements can serve to highlight the flowtrajectory path. FIG. 4(b) illustrates a healthy carotid bifurcationscenario without any visualization enhancement. FIGS. 12a to 12d showsshows a set of flow speckle frames displayed without the vectorprojectiles. When visualized form of a high frame rate cineloop wellbeyond the video display range, these flow speckles would displacecoherently in between frames according to the pulsatile flow pattern.This form of rendering would depict the flow trajectory accordingly. Inturn, when displayed concurrently with the vector projectiles, theywould provide a secondary visualization channel for complex flowinformation.

FIGS. 13a-13d shows the same flow as in FIG. 12, but in this case thevector projectiles are shown without the speckles. The finished displaywith speckles and projectiles is shown in FIG. 6.

Being a newly developed technique with fine temporal resolution and flowvector estimation capabilities, VPI can be leveraged to investigatevarious forms of complex flow dynamics. For instance, besides using VPIto study flow patterns in the carotid bifurcation as demonstrated here,this technique can be used to examine multi-directional flow dynamicsinside diseased vascular features such as aneurysms. Also, VPI can beapplied to visualize flow turbulence with fluttering features thatrequire fine temporal resolution to render coherently. Realizing theseapplications would effectively substantiate the diagnostic value of VPIin complex flow analysis.

As the fine temporal resolution offered by VPI hinges on the use ofbroad-view data acquisition sequences in which the ultrasound firingsare unfocused in nature, the flow signals returned from deepervasculatures would inevitably be weaker as a consequence. This issue,which would be physically worsened by depth dependent attenuation, maypose a challenge when diagnosing certain patients whose vasculaturetends to be positioned farther away from the skin surface. Hence, flowsignal enhancement techniques may be used to reinforce the efficacy ofthe VPI framework when used in different in-vivo scan settings. Oneparticular strategy that can be used is the incorporation of codedexcitation principles into the transmission pulse sequence design. SeeZhao H, Mo L Y L, Gao S, “Barker-coded ultrasound color flow imaging:Theoretical and practical design considerations,” IEEE Trans UltrasonFerroelectr Freq Control (2007), 54:319-331, which is incorporatedherein in its entirety. Alternatively, microbubble contrast agents maybe introduced to boost the flow signal level when performing VPI. See,Tremblay-Darveau C, Williams R, Milot L, Bruce M, Burns P N, “UltrafastDoppler imaging of microbubbles,” In Proceedings 2012 IEEE UltrasonicsSymposium, Dresden, Germany, 7-10 October. New York: IEEE; (2012), p.1315-1318.

Another aspect of VPI to be further refined is its engineeringconsiderations regarding the technique's real time realization. In thearrangement of FIG. 10, real-time GPU-based beam formers were leveraged,but the data were processed off-line because the scanner hardware wasbased on the use of a universal serial bus data transfer link whosebandwidth was inadequate for real-time streaming. To effectivelyfacilitate on-line execution of VPI, a high-speed data transferconnection (e.g., Peripheral Component Interconnect Express links) maybe used, e.g., with ultrasound scanner architectures that supportchannel-domain data streaming at real-time throughputs. See, Diagle R E,Kaczdowski P J, “High frame rate quantitative Doppler flow imaging usingunfocused transmit beams,” U.S. patent application Ser. No. 12/490,780(2009); and Walczak M, Lewandowski M, Zolek N, “Optimization ofreal-time ultrasound PCI e data streaming and Open CL processing forSAFT imaging,” In Proceedings, 2013 IEEE Ultrasonics Symposium, Prague,Czech Republic, 21-25 July. New York: IEEE; (2013), both of which areincorporated herein in their entirety.

Alternatively, VPI can be further used for echocardiographyinvestigations where vector visualization of intracardiac flow fieldscurrently relies on either post-processing of color flow imaging data orthe use of microbubble contrast agents to perform echo particle imagevelocimetry. To realize VPI for echocardiography applications, the flowvector estimation framework would need to be further refined to accountfor the non-stationary tissue clutter that arises due to myocardialcontraction. For instance, when deriving the frequency shift estimatesof each Tx-Rx angle pair, advanced signal processing solutions that areresilient against tissue motion biases could be adapted for thispurpose, such as maximum likelihood estimation and adaptive-rankeigen-estimation. See, Lovstakken L, Bjaerum S, Torp H, “Optimalvelocity estimation in ultrasound color flow imaging in presence ofclutter,” IEEE Trans. Ultrason. Ferroelec. Freq. Contr., (2007), 54:539-549; and Yu ACH, Cobbold RSC, “Single-ensemble-basedeigen-processing methods for color flow imaging—Part II. The matrixpencil estimator,” IEEE Trans. Ultrason. Ferroelec. Freq. Contr.,(2008), 55: 573-587, both of which are incorporated herein in theirentirety.

VPI can be considered a new approach in leveraging ultrasound for flowestimation purposes. In particular, it represents a drastictransformation in the way that flow information is acquired, estimated,and rendered in comparison to conventional color flow imaging. Since VPIis essentially non-invasive, this technique should hold promise in beingintroduced as a routine diagnostic tool to investigate complex flowdynamics in the human vasculature. For instance, in the context ofcarotid diagnostics, VPI can potentially be adopted as a moreinstinctive way to assess the severity of carotid stenosis compared withthe conventional Doppler spectrogram mode that is routinely performed aspart of the clinical practice for carotid disease management. If suchclinical translation effort can be realized, the present role ofultrasound in vascular diagnostics can undoubtedly be expanded.

The invention is not to be limited in scope by the specific embodimentsdescribed herein. Indeed, various modifications of the invention inaddition to those described will become apparent to those skilled in theart from the foregoing description and accompanying figures. Suchmodifications are intended to fall within the scope of the appendedclaims.

1-10. (canceled)
 11. An ultrasound imaging system comprising: a dataacquisition unit, which transmits, via an ultrasonic array transducer, aseries of plane waves into a tissue and receives waves reflected fromthe tissue to obtain beam-formed data frames; a flow vector estimationunit which estimates flow vectors at pixels of the data frames usingdata of the data frames; and a display rendering circuit which displays,on a display, the flow vectors estimated as color coded movingprojectiles having varying lengths or colors themselves across themoving projectiles based on velocity magnitudes of one or more flowvectors of the flow vectors corresponding to the moving projectiles,wherein positions of the projectiles are dynamically updated betweendata frames based on the flow vectors corresponding to the projectilesand one or more inter-frame periods between the data frames to depictmovement of the projectiles.
 12. The system of claim 11, wherein, as thevelocity magnitudes of the one or more flow vectors increase, the colorsof the moving projectiles corresponding to the one or more flow vectorsbecome brighter.
 13. The system of claim 11, wherein, as the velocitymagnitudes of the one or more flow vectors increase, the lengths of themoving projectiles corresponding to the one or more flow vectors becomelonger.
 14. The system of claim 11, wherein direction of the projectilesshows flow direction at the pixels.
 15. The system of claim 11, whereinthe display rendering circuit displaying the flow vectors estimated asmoving projectiles comprises: selecting a set of pixels in a data frameas projectile launch points; displaying the flow vectors at the set ofpixels selected as projectiles; calculating incremental displacement ofthe next frame based on the corresponding axial and lateral velocitiesof the projectiles and the one or more inter-frame periods; updatingpositions of projectiles in the next frame based on the displacementcalculated; and displaying projectiles of the next frame at thepositions updated.
 16. The system of claim 11, wherein a projectile isdisplayed only if its instantaneous pixel position falls within a flowregion.
 17. The system of claim 11, wherein, when an instantaneous pixelposition of a projectile does not fall within a flow region, a newprojectile is regenerated at an original projectile launch point of thisprojectile.
 18. The system of claim 11, wherein the display renderingcircuit further displays grayscale flow speckles together with theprojectiles.
 19. An ultrasound imaging system comprising: a dataacquisition unit, which transmits, via an ultrasonic array transducer, aseries of unfocused waves into a tissue and receives waves reflectedfrom the tissue to obtain beam-formed data frames; a flow vectorestimation unit which estimates flow vectors at pixels of the dataframes using data of the data frames; and a display rendering circuitwhich displays, on a display, the flow vectors estimated as movingprojectiles having varying lengths or colors themselves across themoving projectiles based on velocity magnitudes of one or more flowvectors of the flow vectors corresponding to the moving projectiles,wherein positions of the projectiles are dynamically updated betweendata frames based on the flow vectors corresponding to the projectilesand one or more inter-frame periods between the data frames to depictmovement of the projectiles.
 20. The system of claim 19, wherein theunfocused waves include plane waves or divergent waves.
 21. The systemof claim 19, wherein, as the velocity magnitudes of the one or more flowvectors increase, the colors of the moving projectiles corresponding tothe one or more flow vectors become brighter.
 22. The system of claim19, wherein, as the velocity magnitudes of the one or more flow vectorsincrease, the lengths of the moving projectiles corresponding to the oneor more flow vectors become longer.
 23. An ultrasound imaging systemcomprising: a data acquisition unit, which transmits, via an ultrasonicarray transducer, a series of plane waves into a tissue and receiveswaves reflected from the tissue to obtain beam-formed data frames; aflow vector estimation unit which estimates flow vectors at pixels ofthe data frames using data of the data frames; and a display renderingcircuit which displays, on a display, the flow vectors estimated asmoving projectiles having varying lengths or colors themselves acrossthe moving projectiles based on velocity magnitudes of one or more flowvectors of the flow vectors corresponding to the moving projectiles,wherein positions of the projectiles are dynamically updated betweendata frames based on the flow vectors corresponding to the projectilesand one or more inter-frame periods between the data frames to depictmovement of the projectiles.